Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction

TL;DR

This paper investigates how weak spin-orbit interactions influence chaotic quantum transport, providing a unified semiclassical theory for the entire symmetry crossover regime and validating it with numerical simulations.

Contribution

It introduces a semiclassical framework that describes the symmetry crossover in quantum transport due to spin-orbit interaction, including new analytical formulas and numerical validation.

Findings

Derived analytical expressions for conductance, variance, and shot noise across the crossover.

Validated semiclassical results with numerical simulations of a random matrix model.

Unified description of symmetry crossover from GOE to GSE regimes.

Abstract

We study a chaotic quantum transport in the presence of a weak spin-orbit interaction. Our theory covers the whole symmetry crossover regime between time-reversal invariant systems with and without a spin-orbit interaction. This situation is experimentally realizable when the spin-orbit interaction is controlled in a conductor by applying an electric field. We utilize a semiclassical approach which has recently been developed. In this approach, the non-Abelian nature of the spin diffusion along a classical trajectory plays a crucial role. New analytical expressions with one crossover parameter are semiclassically derived for the average conductance, conductance variance and shot noise. Moreover numerical results on a random matrix model describing the crossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (Gaussian Symplectic Ensemble) are compared with the semiclassical expressions.